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Predicting temperature curve based on fast kNN local linear estimation of the conditional distribution function.

Ibrahim M Almanjahie^1,2, Zoulikha Kaid^1,2, Ali Laksaci^1,2

¹Department of Mathematics, College of Science, King Khalid University, Abha, South Region, Saudi Arabia.

|July 21, 2021

Summary

This study introduces novel functional time series methods for accurate temperature prediction, crucial for climate change impact assessment. The research compares two estimators to enhance meteorological data analysis and predictive modeling.

Keywords:

Conditional predictive region Distribution function Functional time series Kernel weighting Local linear fitting Meteorological data k-nearest neighbors smoothing

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Area of Science:

Statistics
Meteorology
Climate Science

Background:

Accurate temperature prediction is vital for understanding climate change impacts on ecosystems and human populations.
Traditional statistical models struggle with large meteorological datasets due to dimensionality issues.
Functional time series analysis offers a promising alternative for handling complex temporal data.

Purpose of the Study:

To address the predictive region problem in functional time series analysis for meteorological data.
To develop and compare two novel estimators for conditional distribution functions.
To evaluate the efficiency and feasibility of these estimators in predicting yearly temperature curves.

Main Methods:

Utilized local linear estimation of the cumulative function with a functional input variable.
Combined the k-Nearest Neighbors (k-NN) procedure with local linear algorithms to create two distinct estimators.
Employed a simulation study to assess estimator efficiency based on dependence levels.
Applied the methods to real meteorological data for comparative analysis of predictive regions.

Main Results:

The study successfully developed two estimators for conditional distribution functions within functional time series analysis.
Comparative simulations demonstrated the efficiency of the proposed estimators concerning varying dependence levels.
The shortest conditional modal interval predictive regions were effectively computed using real meteorological data.

Conclusions:

The developed functional time series methods offer a viable approach for accurate temperature prediction.
The k-NN combined with local linear estimation provides efficient tools for meteorological data analysis.
These methods enhance our ability to model and predict climate change impacts through improved temperature forecasting.